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ICS 180: Digital Signal Processing

Aditi Majumder

Instructor

• Aditi Majumder

• Room: CS 352C

• Email: majumder@ics.uci.edu

• Website: http://www.ics.uci.edu/~majumder/DSP/dsp.htm

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The Course

• Fun course

• You will implement things and see results

• Digital Image Processing

• Do not worry about grades, enjoy the course

• Tell your friends

Course Load

• Learn about both 1D and 2D

• Programming Assignments mostly on 2D– Image Processing

• Written Assignments

• Midterm: 12 May (Wednesday)

• Finals

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Logistics

• No late homework submission• No fixed office hours

– Send me email

• Grading Policy– Programming Assignments: 30%– Written Assignments: 10%– Midterm: 30%– Finals: 30%

Syllabus

• Signals and Linear Systems (0.5)• Convolution and Properties (2)• Fourier Transform and Properties (3)• Continuous Signal Processing (0.5)• Applications to Audio and Image

Processing (4)• Text: The Scientist and Engineer’s

Guide to Digital Signal Processing, Steven W. Smith

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Hands On Experience

• Filtering (Low, high, and band pass)

• Edge Crispening

• Edge Detection

• Feature Detection

• Noise Cleaning

• FFT and Convolution

• Image Resampling

• Image Morphology

What is a signal?

• Any function dependent on a single or multiple variables

t

Am

pli

tud

e

1D: A = f ( t )

x

y

2D: I = f ( x, y )

x

y

z

3D: M = f ( x, y, z )

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Origin of Signals

• Real life applications– Medical Images

– Seismic Vibrations

– Audio and Video

– Radar and Sonar

Signal Processing

• Science of processing signals– Data analysis

– Data compression

– Data Storage

– Data Retrieval

– Data Communication

– Special Effects

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Applications

• Space– Photo Enhancement, Segmentation

• Medical– Diagnostic image analysis

• Media– Audio and video compression, Quality Control

• Military– Radar and sonar data analysis

• Scientific– Emergency monitoring and analysis

Analog Signals

• Both independent and dependent variables can assume a continuous range of values

• Exists in nature

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Digital Signals

• Both independent and dependent variables are discretized

• Representation in computers

• Sampling– Discrete independent variable

– Sample and hold (S/H)

• Quantization– Discrete dependent variable

– Analog to Digital Converter (ADC)

Digital Signal

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Sampled Signal

Digitized Signal

•Depends on number of bits•12 bits = 4095 levels• 0.0 ≤ Voltage ≤4.096•2.56 and 2.5601 TO 2560•Each level (LSB) = 0.001•Error ≤ ±½ LSB•Called Quantization Error

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Digitized Signal

•Depends on number of bits•12 bits = 4095 levels• 0.0 ≤ Voltage ≤4.096•2.56 and 2.5601 TO 2560•Each level (LSB) = 0.001•Error ≤ ±½ LSB•Called Quantization Error

Quantization Error

• Usually like random noise

• Noise is present in most signal acquisition systems

• Random uncorrelated samples added to the original signal

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Proper Sampling

• If the original signal can be reconstructed unambiguously from the sampled signal

Cycles/ Sample =Number of cycles per second

Number of samples per second

=Analog Frequency

Sampling Rate

Is it Proper Sampling?

• DC signal

• Freq = 0.0 x Sampling Rate

• Proper

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Is it Proper Sampling?

• Freq = 0.09 x Sampling Rate

• Each sample covers 0.09 cycles

• Proper

Is it Proper Sampling?

• Freq = 0.31 x Sampling Rate

• Larger fraction of cycles per sample

• Proper

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Is it Proper Sampling?

• Freq = 0.95 x Sampling Rate

• Much larger parts of cycles per sample

• Not Proper

• Aliasing

• Changes frequency and phase

Sampling Theorem

• Proper Sampling: At least one sample per half cycle

• Freq ≤ 0.5 x Sampling Rate

• Sampling Rate ≥ 2 x Frequency

• Nyquist Rate

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Time (Spatial) Domain vs. Frequency Domain

• Any one dimensional analog signal can be represented as a linear combination of sine waves of different frequencies

1D Signal

• Example: Once scan line of an image

• Amount of each sine wave defined by its amplitude and phase